Missing data imputation
Demographics | Physical health | Hearing | Cognition | Mobility and balance | Quality of life | Mental health | Social participation and support | Views on hearing loss |
Background
Why impute missing data?
Logistic regression and other statistical methods require complete cases. In our case, with 40+ variables of interest, dropping participants with any missing values leads to a sample size of 200+ cases instead of 500+. There is loss of power, and estimates from models will likely be biased. The goal of missing data imputation is to restore variance of the sample to make it better reflect characteristics of the population (i.e., give accurate estimates of standard errors, CI’s, and p-values).
MICE procedure
‘Multiple Imputation by Chained Equations’
Say there are three variables ‘A’, ‘B’, and ‘C’, each with some missing values. Choose variable ‘A’ to start filling in. Fill in missing values in ‘B’ and ‘C’ with temporary values, such as the mean.
Make an equation A ~ B + C, using observed cases of ‘A’ to predict missing values of ‘A’, including a random component. Move on to predicting missing ‘B’, using B ~ A + C and including predicted ‘A’, again including a random component. Move on to predicting missing ‘C’, using C ~ A + B and predicted ‘A’ and ‘B’. This is one cycle.
Choose the number of cycles, say 10 iterations. At the end of 10 iterations, an “imputed” dataset is formed with no missing values. Choose the number of imputed datasets to form (the same analysis will be conducted on each slightly different dataset, and the results will be pooled). Choose which variables should be used as predictors of other variables. Choose which method to use for predicting missing values, e.g., predictive mean matching. For derived variables such as summed scores, consider whether to impute components first and then calculate derived scores, or impute derived scores. Consider whether there should be an order of which variables to start imputing first.
Check whether the imputed data “converge” (the means and SEs stabilize after a few iterations, and are similar across imputed datasets). Check the distributions and characteristics of imputed data (e.g. integer-only values, floors and ceilings, plausibility), and their similarity to observed data.
1. Pre-imputation work
(i) Evaluate missingness
Variables of interest
Demographics: Age, Gender, Work, Volunteer, Live alonePhysical health: Rating, Multimorbidity score, Subjective vision (loss, rating aided), Subjective hearing (loss, rating aided, rating unaided)
Hearing health: Hearing device use, Hearing device type, Tinnitus past 7 days, 15i-SSQ mean score, SIM mean score, EmoCheQ mean score, HHIE-S total score, BPTA4
Cognitive health: Subjective cognitive impairment, CSRQ mean score
Mobility and balance: Mobility aid use, ABC (balance confidence) mean score
Quality of life: SWLS mean score, WHO overall QoL, WHO health QoL, WHO money, WHO four domains
Mental health: PHQ4, split into anxiety and depression subscores
Social factors: Loneliness, Social Network Index, Social Participation Frequency, Social Participation Types, Social Support MOS mean score
Views: Connections total correct score, Motivations mean score
% Missing data within participants
##
## The decimal point is at the |
##
## 0 | 00004444444444444444444444444444444444444999999999999999999999999999+193
## 2 | 22222222222222222222222222222222222222222277777777777777777777777777+16
## 4 | 000044444999993333333888888888888
## 6 | 222222222222222666666666666666666111111111111111111155555555555
## 8 | 0000000004444888833337777
## 10 | 221199
## 12 | 488
## 14 | 2055
## 16 | 47
## 18 | 65
## 20 |
## 22 | 5
## 24 | 2
## 26 |
## 28 |
## 30 |
## 32 |
## 34 |
## 36 |
## 38 |
## 40 |
## 42 | 9
## 44 |
## 46 |
## 48 |
## 50 |
## 52 |
## 54 |
## 56 |
## 58 |
## 60 | 6
## 62 |
## 64 | 6
## 66 | 87
## 68 |
## 70 | 8827
## 72 | 6
## 74 | 337
## 76 | 0
## 78 |
## 80 | 5
## 82 |
## 84 |
## 86 |
## 88 |
## 90 | 6
## 92 |
## 94 |
## 96 |
## 98 | 66Missing data patterns
Participants with <26% missing data (n=509): 
Participants with >42% missing data (n=18): 
(ii) Data cleaning
Rules
- For “single-item” variables (e.g. loneliness): NA’s are left as
is.
- For co-morbidity checklist: All responses other than “yes” (NA’s,
No, Don’t know) are treated as “no”.
- For composite variables: If a participant has “NA” for all items,
the composite score is also “NA”.
- WHOQOL-BREF: Follow their protocol for NA’s.
- For SIM, EmoCheQ, CSRQ, PHQ4, Views on motivations: Impute case
mean.
- For 15i-SSQ: Impute case mean within subscale.
- For HHIES: Impute case mode within subscale.
- For ABC: Recode NA’s to 0 (single participant).
- For Social Network Index: Recode NA’s to “never”.
- For Social Participation: Recode NA’s to “never”.
- For Social Support: Recode NA’s to “none”.
- For Views (Connections): Drop foil item; only correct items
credited.
- For Views (Motivations): Impute mean.
(iii) Evaluate missingness again
% Missing data within participants
##
## The decimal point is at the |
##
## 0 | 00000000000000000000000000000000000000000000000000000000000000000000+151
## 2 | 22222222222222222222222222222222222222222222222222222222222222222222+51
## 4 | 333333333333333333333333333333333333333333333
## 6 | 555555555555555555555555555555555555555555555555555555555
## 8 | 777777777777777777777777777
## 10 | 99999999999
## 12 | 00000
## 14 |
## 16 | 4
## 18 | 6
## 20 |
## 22 |
## 24 |
## 26 |
## 28 |
## 30 |
## 32 |
## 34 |
## 36 |
## 38 |
## 40 | 3
## 42 |
## 44 |
## 46 |
## 48 |
## 50 | 0
## 52 | 22
## 54 | 3
## 56 |
## 58 | 7777
## 60 | 999
## 62 |
## 64 | 2
## 66 |
## 68 | 6
## 70 | 7
## 72 |
## 74 |
## 76 | 1
## 78 |
## 80 |
## 82 |
## 84 |
## 86 |
## 88 |
## 90 | 33Missing data patterns
Participants with <20% missing data (n=509):
## # A tibble: 45 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 Gender_bin 0 0
## 2 Age 2 0.393
## 3 Retired_bin 0 0
## 4 Volunteer 0 0
## 5 Lives_alone_bin 0 0
## 6 Phys_health_rating 7 1.38
## 7 Multimorbidity_score 0 0
## 8 Subj_vision_loss_bin 18 3.54
## 9 Subj_vision_rating_aided 1 0.196
## 10 Subj_hearing_loss_bin 36 7.07
## 11 any_hearing_device 0 0
## 12 study2_HA 0 0
## 13 Subj_hearing_rating_aided_REV 159 31.2
## 14 Subj_hearing_rating_unaided_REV 8 1.57
## 15 Tinnitus_past_wk_bin 0 0
## 16 ssq_speech_REV 46 9.04
## 17 ssq_spatial_REV 51 10.0
## 18 ssq_qualities_REV 3 0.589
## 19 SIM_mean 12 2.36
## 20 Emocheq_mean 8 1.57
## 21 hhies_emo_total 0 0
## 22 hhies_soc_total 0 0
## 23 positive_SCI_bin 0 0
## 24 CSRQ_mean 0 0
## 25 Mobility_needs_bin 0 0
## 26 ABC_mean 0 0
## 27 SWLS_mean 0 0
## 28 WHOQOL_overall_qol 0 0
## 29 WHOQOL_health_qol 0 0
## 30 WHOQOL_Dom1_phys 0 0
## 31 WHOQOL_Dom2_psy 0 0
## 32 WHOQOL_Dom3_soc 1 0.196
## 33 WHOQOL_Dom4_env 0 0
## 34 WHO_money 0 0
## 35 PHQ4_anx_mean 1 0.196
## 36 PHQ4_dep_mean 1 0.196
## 37 Lonely_bin 1 0.196
## 38 Social_network_index 1 0.196
## 39 Soc_part_freq 1 0.196
## 40 Soc_part_types 1 0.196
## 41 Socsupp_mean 5 0.982
## 42 Connections_total 9 1.77
## 43 Motivate_mean 5 0.982
## 44 study1_HA_bin 78 15.3
## 45 PTA4_better_ear 73 14.3Participants with >39%% missing data (n=18):
(iv) Justify discarding/retaining participants
Drop 2 cases that are fully missing
## Progress Duration.in.seconds Finished
## 458 0 217 0
## 467 1 540 0## # A tibble: 46 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 Gender_bin 2 100
## 2 Age 2 100
## 3 Retired_bin 2 100
## 4 Volunteer 2 100
## 5 Lives_alone_bin 2 100
## 6 Phys_health_rating 2 100
## 7 Multimorbidity_score 0 0
## 8 Subj_vision_loss_bin 2 100
## 9 Subj_vision_rating_aided 2 100
## 10 Subj_hearing_loss_bin 2 100
## 11 any_hearing_device 0 0
## 12 study2_HA 0 0
## 13 Subj_hearing_rating_aided_REV 2 100
## 14 Subj_hearing_rating_unaided_REV 2 100
## 15 Tinnitus_past_wk_bin 0 0
## 16 ssq_speech_REV 2 100
## 17 ssq_spatial_REV 2 100
## 18 ssq_qualities_REV 2 100
## 19 SIM_mean 2 100
## 20 Emocheq_mean 2 100
## 21 hhies_emo_total 2 100
## 22 hhies_soc_total 2 100
## 23 positive_SCI_bin 2 100
## 24 CSRQ_mean 2 100
## 25 Mobility_needs_bin 2 100
## 26 ABC_mean 2 100
## 27 SWLS_mean 2 100
## 28 WHOQOL_overall_qol 2 100
## 29 WHOQOL_health_qol 2 100
## 30 WHOQOL_Dom1_phys 2 100
## 31 WHOQOL_Dom2_psy 2 100
## 32 WHOQOL_Dom3_soc 2 100
## 33 WHOQOL_Dom4_env 2 100
## 34 WHO_money 2 100
## 35 PHQ4_anx_mean 2 100
## 36 PHQ4_dep_mean 2 100
## 37 Lonely_bin 2 100
## 38 Social_network_index 2 100
## 39 Soc_part_freq 2 100
## 40 Soc_part_types 2 100
## 41 Socsupp_mean 2 100
## 42 Connections_total 2 100
## 43 Motivate_mean 2 100
## 44 study1_HA_bin 2 100
## 45 PTA4_better_ear 2 100
## 46 PTA4_asym 2 100Retain 16 that mostly have age, audiogram, earlier measures
## Progress Duration.in.seconds Finished
## 45 58 413 0
## 77 19 247 0
## 136 58 308782 0
## 153 30 449 0
## 166 52 185 0
## 176 53 1693 0
## 187 53 518035 0
## 192 45 504174 0
## 228 13 96 0
## 246 64 1719 0
## 318 55 466 0
## 364 55 988 0
## 405 55 650 0
## 483 45 731 0
## 520 64 6724 0
## 522 70 2376 0## # A tibble: 46 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 Gender_bin 0 0
## 2 Age 1 6.25
## 3 Retired_bin 0 0
## 4 Volunteer 0 0
## 5 Lives_alone_bin 0 0
## 6 Phys_health_rating 2 12.5
## 7 Multimorbidity_score 0 0
## 8 Subj_vision_loss_bin 2 12.5
## 9 Subj_vision_rating_aided 2 12.5
## 10 Subj_hearing_loss_bin 3 18.8
## 11 any_hearing_device 0 0
## 12 study2_HA 0 0
## 13 Subj_hearing_rating_aided_REV 8 50
## 14 Subj_hearing_rating_unaided_REV 3 18.8
## 15 Tinnitus_past_wk_bin 0 0
## 16 ssq_speech_REV 13 81.2
## 17 ssq_spatial_REV 11 68.8
## 18 ssq_qualities_REV 6 37.5
## 19 SIM_mean 11 68.8
## 20 Emocheq_mean 11 68.8
## 21 hhies_emo_total 13 81.2
## 22 hhies_soc_total 13 81.2
## 23 positive_SCI_bin 13 81.2
## 24 CSRQ_mean 15 93.8
## 25 Mobility_needs_bin 15 93.8
## 26 ABC_mean 15 93.8
## 27 SWLS_mean 15 93.8
## 28 WHOQOL_overall_qol 16 100
## 29 WHOQOL_health_qol 16 100
## 30 WHOQOL_Dom1_phys 16 100
## 31 WHOQOL_Dom2_psy 16 100
## 32 WHOQOL_Dom3_soc 16 100
## 33 WHOQOL_Dom4_env 16 100
## 34 WHO_money 16 100
## 35 PHQ4_anx_mean 16 100
## 36 PHQ4_dep_mean 16 100
## 37 Lonely_bin 16 100
## 38 Social_network_index 16 100
## 39 Soc_part_freq 16 100
## 40 Soc_part_types 16 100
## 41 Socsupp_mean 16 100
## 42 Connections_total 16 100
## 43 Motivate_mean 16 100
## 44 study1_HA_bin 3 18.8
## 45 PTA4_better_ear 3 18.8
## 46 PTA4_asym 3 18.8(v) Variable relationships
Correlations heatmap: Hearing
Correlations heatmap: Physical health
PCA
Note: PC1 and PC2 account for 36% of the total variance.
2. Imputation using MICE
Current method
- Use predictors that correlate 0.5 or better to impute missing data
in a variable (30 variables); if no such predictors, adjust threshold to
0.4 (3 variables), then 0.3, then 0.2 (2 variables)
pdf
- Eight variables are complete and do not require imputing; 2
variables have no predictors that correlate at least r = 0.2
(Subj_vision_loss_bin, Connections_total)
- MICE settings: total of 5 imputed datasets, with a maximum of 10 iterations per dataset, using predictive means matching to impute missing values
Check imputed data
PCA with standardized imputed data
PCA
Note: This is only 1 of 5 imputed datasets, but the plots are similar.
3. Predicting hearing aid adoption
Complete cases vs. imputed data
Note: All participants together; not filtered by hearing aid candidacy.
Regression output (complete cases, n=346)
Non-hearing aid users = 267
Hearing aid users = 79 (22.8%)
Note: Dropped Subj_hearing_rating_aided_REV & SWLS_mean due to VIF
> 5
## Term Estimate StdError z p OddsRatio CIlower CIupper
## 1 (Intercept) -24.5645 884.2355 -0.0278 0.9778 0.0000 0.0000 Inf
## 2 Gender_bin 0.5265 0.4564 1.1536 0.2487 1.6930 0.6921 4.1418
## 3 Age -0.0185 0.0346 -0.5336 0.5936 0.9817 0.9172 1.0506
## 4 Retired_bin 0.0571 0.5098 0.1121 0.9108 1.0588 0.3898 2.8757
## 5 Volunteer_rec 0.5477 0.2816 1.9448 0.0518 1.7293 0.9957 3.0031
## 6 Lives_alone_bin -0.2751 0.5566 -0.4943 0.6211 0.7595 0.2551 2.2608
## 7 Phys_health_rating 0.0966 0.3728 0.2590 0.7956 1.1014 0.5304 2.2868
## 8 Multimorbidity_score -0.0199 0.1206 -0.1652 0.8688 0.9803 0.7739 1.2417
## 9 Mobility_needs_bin -0.3204 1.1148 -0.2874 0.7738 0.7258 0.0816 6.4536
## 10 ABC_mean -0.0315 0.0261 -1.2055 0.2280 0.9690 0.9206 1.0199
## 11 Subj_vision_rating_aided 0.0508 0.2960 0.1717 0.8637 1.0521 0.5890 1.8795
## 12 Subj_hearing_loss_bin 17.0709 884.2210 0.0193 0.9846 25929967.6016 0.0000 Inf
## 13 Subj_hearing_rating_unaided_REV 1.0591 0.3850 2.7506 0.0059 2.8837 1.3559 6.1334
## 14 Tinnitus_past_wk_bin 0.1555 0.4104 0.3790 0.7047 1.1683 0.5227 2.6112
## 15 PTA4_better_ear 0.1214 0.0288 4.2225 0.0000 1.1291 1.0672 1.1945
## 16 PTA4_asym 0.0472 0.0153 3.0891 0.0020 1.0483 1.0174 1.0802
## 17 SSQ15i_mean_REV -0.6680 0.1855 -3.6002 0.0003 0.5128 0.3564 0.7376
## 18 Emocheq_mean -0.0308 0.2780 -0.1108 0.9118 0.9697 0.5623 1.6721
## 19 HHIES_total 0.0596 0.0386 1.5445 0.1225 1.0614 0.9841 1.1448
## 20 SIM_mean -0.1358 0.1165 -1.1662 0.2435 0.8730 0.6948 1.0968
## 21 positive_SCI_bin 1.1976 0.7118 1.6824 0.0925 3.3122 0.8207 13.3674
## 22 CSRQ_mean -0.1344 0.6195 -0.2170 0.8282 0.8742 0.2596 2.9440
## 23 PHQ4_anx_mean 1.5003 0.4999 3.0009 0.0027 4.4829 1.6827 11.9431
## 24 PHQ4_dep_mean -1.1449 0.6681 -1.7137 0.0866 0.3183 0.0859 1.1788
## 25 WHOQOL_overall_qol -0.4355 0.4717 -0.9233 0.3558 0.6469 0.2567 1.6306
## 26 WHOQOL_health_qol 0.3760 0.3228 1.1648 0.2441 1.4565 0.7736 2.7421
## 27 WHO_money 0.8039 0.2691 2.9869 0.0028 2.2343 1.3184 3.7865
## 28 Socsupp_mean 0.2161 0.2994 0.7216 0.4705 1.2412 0.6902 2.2320
## 29 Social_network_index -0.1362 0.1756 -0.7754 0.4381 0.8727 0.6185 1.2313
## 30 Soc_part_freq -0.2681 0.3671 -0.7303 0.4652 0.7648 0.3724 1.5706
## 31 Soc_part_types 0.0183 0.1582 0.1155 0.9080 1.0184 0.7469 1.3886
## 32 Lonely_bin -0.2511 0.6864 -0.3658 0.7145 0.7780 0.2026 2.9868
## 33 Motivate_mean 0.3051 0.2395 1.2743 0.2026 1.3568 0.8486 2.1694Regression output (imputed data, n=525)
## Term Estimate StdError t df p OddsRatio CIlower CIupper
## 1 (Intercept) -0.6315 0.3524 -1.7921 276.6114 0.0742 0.5318 0.2665 1.0610
## 2 Gender_bin 0.0568 0.0364 1.5602 464.2247 0.1194 1.0584 0.9856 1.1367
## 3 Age 0.0025 0.0025 0.9939 368.6422 0.3209 1.0025 0.9976 1.0074
## 4 Retired_bin -0.0288 0.0369 -0.7805 489.2480 0.4355 0.9716 0.9038 1.0445
## 5 Volunteer_rec 0.0441 0.0206 2.1351 465.5042 0.0333 1.0451 1.0037 1.0881
## 6 Lives_alone_bin -0.0227 0.0422 -0.5367 441.5722 0.5918 0.9776 0.9000 1.0618
## 7 Phys_health_rating -0.0024 0.0276 -0.0876 255.2605 0.9303 0.9976 0.9451 1.0531
## 8 Multimorbidity_score 0.0044 0.0077 0.5713 485.2053 0.5680 1.0044 0.9894 1.0197
## 9 Mobility_needs_bin -0.0268 0.0880 -0.3049 209.2891 0.7607 0.9736 0.8193 1.1568
## 10 ABC_mean -0.0032 0.0017 -1.9151 340.0681 0.0563 0.9968 0.9935 1.0001
## 11 Subj_vision_rating_aided 0.0102 0.0234 0.4366 461.3953 0.6626 1.0103 0.9650 1.0577
## 12 Subj_hearing_loss_bin 0.0967 0.0509 1.8974 250.9344 0.0589 1.1015 0.9969 1.2171
## 13 Subj_hearing_rating_unaided_REV 0.0969 0.0253 3.8330 470.9501 0.0001 1.1018 1.0484 1.1578
## 14 Tinnitus_past_wk_bin -0.0540 0.0348 -1.5504 478.5980 0.1217 0.9474 0.8850 1.0143
## 15 PTA4_better_ear 0.0077 0.0023 3.3060 67.9205 0.0015 1.0077 1.0032 1.0123
## 16 PTA4_asym 0.0028 0.0015 1.8414 96.0029 0.0686 1.0028 0.9999 1.0058
## 17 SSQ15i_mean_REV -0.0681 0.0134 -5.0894 450.3870 0.0000 0.9342 0.9100 0.9590
## 18 Emocheq_mean -0.0051 0.0218 -0.2358 305.8811 0.8137 0.9949 0.9533 1.0383
## 19 HHIES_total 0.0063 0.0031 2.0697 133.4496 0.0404 1.0063 1.0002 1.0125
## 20 SIM_mean -0.0037 0.0086 -0.4279 151.9795 0.6693 0.9963 0.9797 1.0132
## 21 positive_SCI_bin 0.0445 0.0596 0.7467 242.5054 0.4560 1.0455 0.9302 1.1751
## 22 CSRQ_mean -0.0476 0.0499 -0.9535 295.2604 0.3411 0.9535 0.8647 1.0515
## 23 PHQ4_anx_mean 0.1187 0.0375 3.1691 394.3012 0.0016 1.1260 1.0462 1.2119
## 24 PHQ4_dep_mean -0.0099 0.0438 -0.2265 396.3896 0.8209 0.9901 0.9087 1.0789
## 25 WHOQOL_overall_qol 0.0216 0.0339 0.6378 371.0423 0.5240 1.0218 0.9561 1.0920
## 26 WHOQOL_health_qol 0.0262 0.0241 1.0900 212.9481 0.2769 1.0265 0.9792 1.0762
## 27 WHO_money 0.0327 0.0190 1.7210 394.3536 0.0860 1.0332 0.9955 1.0724
## 28 Socsupp_mean 0.0126 0.0244 0.5183 211.7117 0.6048 1.0127 0.9654 1.0623
## 29 Social_network_index -0.0052 0.0142 -0.3641 302.9319 0.7160 0.9948 0.9675 1.0229
## 30 Soc_part_freq 0.0043 0.0280 0.1529 363.5837 0.8786 1.0043 0.9507 1.0610
## 31 Soc_part_types -0.0056 0.0129 -0.4309 350.2229 0.6668 0.9944 0.9696 1.0199
## 32 Lonely_bin -0.0041 0.0492 -0.0834 235.7455 0.9336 0.9959 0.9044 1.0967
## 33 Motivate_mean 0.0172 0.0208 0.8282 205.3380 0.4085 1.0173 0.9767 1.0597Legend: Asterisks denote p < 0.05; crosses denote p [0.05, 0.1]
Accuracy of model predictions
Note: Not really a fair comparison as models and model coefficients are different between complete-cases and imputed data.
## [1] "Complete cases, using median as boundary"## predicted
## actual 0 1
## 0 170 97
## 1 3 76## [1] "Accuracy: 0.711"## [1] "Sensitivity: 0.962"## [1] "Specificity: 0.637"
## [1] "Imputed data, using median as boundary"## predicted
## actual 0 1
## 0 256 166
## 1 7 96## [1] "Accuracy: 0.67"## [1] "Sensitivity: 0.932"## [1] "Specificity: 0.607"Grouping by HHIE-S status
Counts
0-8 no handicap, 10-24 mild to moderate, 26-40 severe
## HHIES
## UseHA None MildMod Sev <NA>
## 0 233 148 30 11
## 1 26 62 13 2
## <NA> 0 0 0 0## [1] 0.100 0.295 0.302 0.154Regression output (imputed data, n=525)
## Term Estimate StdError t df p OddsRatio CIlower CIupper
## 1 (Intercept) 0.1820 0.4579 0.3975 184.9446 0.6915 1.1996 0.4890 2.9432
## 2 Gender_bin -0.0324 0.0425 -0.7629 223.0138 0.4463 0.9681 0.8907 1.0522
## 3 Age -0.0003 0.0030 -0.0901 195.9660 0.9283 0.9997 0.9938 1.0056
## 4 Retired_bin -0.0199 0.0414 -0.4796 220.4080 0.6320 0.9803 0.9039 1.0632
## 5 Volunteer_rec 0.0330 0.0231 1.4277 220.1416 0.1548 1.0336 0.9878 1.0814
## 6 Lives_alone_bin 0.0398 0.0462 0.8619 220.8280 0.3897 1.0406 0.9505 1.1392
## 7 Phys_health_rating -0.0295 0.0316 -0.9338 215.7385 0.3514 0.9709 0.9126 1.0330
## 8 Multimorbidity_score 0.0100 0.0112 0.8994 221.5558 0.3694 1.0101 0.9881 1.0325
## 9 Mobility_needs_bin 0.0200 0.1146 0.1743 214.5812 0.8618 1.0202 0.8150 1.2771
## 10 ABC_mean -0.0013 0.0026 -0.5150 222.9350 0.6070 0.9987 0.9936 1.0038
## 11 Subj_vision_rating_aided -0.0232 0.0283 -0.8191 217.9952 0.4137 0.9771 0.9243 1.0328
## 12 Subj_hearing_loss_bin 0.0907 0.0500 1.8134 221.0009 0.0711 1.0949 0.9927 1.2077
## 13 Subj_hearing_rating_unaided_REV 0.0480 0.0293 1.6373 201.5816 0.1031 1.0492 0.9906 1.1112
## 14 Tinnitus_past_wk_bin -0.0518 0.0426 -1.2149 221.3570 0.2257 0.9495 0.8735 1.0322
## 15 PTA4_better_ear 0.0096 0.0029 3.3417 105.3083 0.0012 1.0096 1.0039 1.0154
## 16 PTA4_asym 0.0043 0.0033 1.2809 29.0812 0.2103 1.0043 0.9978 1.0108
## 17 SSQ15i_mean_REV -0.0507 0.0202 -2.5085 136.4313 0.0133 0.9506 0.9137 0.9890
## 18 Emocheq_mean -0.0075 0.0287 -0.2608 220.4529 0.7945 0.9925 0.9382 1.0500
## 19 HHIES_total 0.0042 0.0075 0.5599 219.0492 0.5761 1.0042 0.9896 1.0191
## 20 SIM_mean 0.0027 0.0094 0.2829 203.4663 0.7775 1.0027 0.9844 1.0213
## 21 positive_SCI_bin 0.1467 0.1061 1.3818 179.8757 0.1687 1.1580 0.9406 1.4257
## 22 CSRQ_mean -0.0401 0.0542 -0.7408 220.0583 0.4596 0.9607 0.8639 1.0684
## 23 PHQ4_anx_mean 0.1012 0.0464 2.1797 215.6318 0.0304 1.1065 1.0103 1.2118
## 24 PHQ4_dep_mean -0.0816 0.0620 -1.3160 190.8040 0.1897 0.9216 0.8162 1.0407
## 25 WHOQOL_overall_qol -0.0135 0.0396 -0.3400 169.8827 0.7342 0.9866 0.9129 1.0662
## 26 WHOQOL_health_qol 0.0028 0.0274 0.1017 202.2451 0.9191 1.0028 0.9504 1.0581
## 27 WHO_money 0.0439 0.0236 1.8575 222.3239 0.0646 1.0449 0.9976 1.0943
## 28 Socsupp_mean 0.0169 0.0288 0.5847 215.6693 0.5593 1.0170 0.9612 1.0761
## 29 Social_network_index -0.0099 0.0154 -0.6442 221.9440 0.5201 0.9901 0.9607 1.0205
## 30 Soc_part_freq -0.0144 0.0339 -0.4240 196.2709 0.6720 0.9857 0.9223 1.0534
## 31 Soc_part_types -0.0068 0.0141 -0.4820 211.5570 0.6303 0.9932 0.9662 1.0211
## 32 Lonely_bin -0.0188 0.0621 -0.3029 215.1029 0.7623 0.9814 0.8689 1.1084
## 33 Motivate_mean -0.0219 0.0236 -0.9263 218.2957 0.3553 0.9783 0.9341 1.0247## Term Estimate StdError t df p OddsRatio CIlower CIupper
## 1 (Intercept) -1.3437 0.5910 -2.2736 120.1590 0.0248 0.2609 0.0819 0.8308
## 2 Gender_bin 0.1154 0.0656 1.7610 190.7221 0.0798 1.1223 0.9869 1.2763
## 3 Age 0.0055 0.0045 1.2130 125.6280 0.2274 1.0055 0.9967 1.0144
## 4 Retired_bin -0.0555 0.0660 -0.8412 216.1656 0.4012 0.9460 0.8312 1.0767
## 5 Volunteer_rec 0.0432 0.0373 1.1577 214.4456 0.2483 1.0441 0.9705 1.1233
## 6 Lives_alone_bin -0.1331 0.0771 -1.7270 214.9260 0.0856 0.8754 0.7526 1.0182
## 7 Phys_health_rating 0.0198 0.0460 0.4290 210.7546 0.6684 1.0200 0.9321 1.1162
## 8 Multimorbidity_score 0.0002 0.0114 0.0177 207.7522 0.9859 1.0002 0.9781 1.0228
## 9 Mobility_needs_bin -0.0133 0.1355 -0.0983 110.1941 0.9219 0.9868 0.7566 1.2870
## 10 ABC_mean -0.0046 0.0023 -1.9778 199.9140 0.0493 0.9954 0.9909 0.9999
## 11 Subj_vision_rating_aided 0.0365 0.0383 0.9537 209.6346 0.3413 1.0372 0.9622 1.1180
## 12 Subj_hearing_loss_bin 0.0962 0.1114 0.8629 156.6792 0.3895 1.1010 0.8850 1.3696
## 13 Subj_hearing_rating_unaided_REV 0.1392 0.0458 3.0388 201.9831 0.0027 1.1494 1.0507 1.2573
## 14 Tinnitus_past_wk_bin -0.0378 0.0561 -0.6736 204.9458 0.5013 0.9629 0.8626 1.0748
## 15 PTA4_better_ear 0.0087 0.0040 2.2070 27.3523 0.0359 1.0087 1.0009 1.0167
## 16 PTA4_asym 0.0027 0.0022 1.2042 33.3114 0.2370 1.0027 0.9984 1.0070
## 17 SSQ15i_mean_REV -0.0731 0.0198 -3.6932 209.1921 0.0003 0.9295 0.8941 0.9663
## 18 Emocheq_mean 0.0079 0.0330 0.2390 213.6771 0.8113 1.0079 0.9448 1.0753
## 19 HHIES_total 0.0035 0.0054 0.6545 151.9871 0.5138 1.0035 0.9929 1.0142
## 20 SIM_mean -0.0196 0.0140 -1.4050 206.7695 0.1615 0.9806 0.9540 1.0079
## 21 positive_SCI_bin 0.0849 0.0837 1.0151 208.2619 0.3112 1.0886 0.9239 1.2827
## 22 CSRQ_mean -0.0362 0.0969 -0.3735 85.0238 0.7097 0.9644 0.7976 1.1662
## 23 PHQ4_anx_mean 0.0908 0.0631 1.4380 174.8102 0.1522 1.0950 0.9677 1.2392
## 24 PHQ4_dep_mean 0.0477 0.0661 0.7216 195.9784 0.4714 1.0489 0.9214 1.1939
## 25 WHOQOL_overall_qol 0.0637 0.0623 1.0229 117.2228 0.3085 1.0658 0.9433 1.2042
## 26 WHOQOL_health_qol 0.0395 0.0406 0.9742 206.4644 0.3311 1.0403 0.9607 1.1265
## 27 WHO_money 0.0224 0.0320 0.6982 108.0940 0.4866 1.0227 0.9605 1.0888
## 28 Socsupp_mean -0.0181 0.0401 -0.4508 175.4000 0.6527 0.9821 0.9078 1.0624
## 29 Social_network_index 0.0009 0.0244 0.0354 213.3367 0.9718 1.0009 0.9542 1.0499
## 30 Soc_part_freq 0.0237 0.0471 0.5032 141.1688 0.6156 1.0240 0.9337 1.1230
## 31 Soc_part_types -0.0044 0.0232 -0.1909 215.6324 0.8488 0.9956 0.9514 1.0419
## 32 Lonely_bin 0.0206 0.0787 0.2614 207.1554 0.7941 1.0208 0.8749 1.1911
## 33 Motivate_mean 0.0714 0.0364 1.9596 170.0572 0.0517 1.0740 1.0001 1.1534Legend: Asterisks denote p < 0.05; crosses denote p [0.05, 0.1]
Grouping by vision status
Counts
##
## 0 1 <NA>
## 215 290 20Regression output (imputed data, n=525)
## Term Estimate StdError t df p OddsRatio CIlower CIupper
## 1 (Intercept) -0.2397 0.5665 -0.4232 177.5691 0.6727 0.7869 0.2592 2.3884
## 2 Gender_bin 0.0265 0.0509 0.5211 175.9306 0.6030 1.0269 0.9294 1.1346
## 3 Age -0.0015 0.0040 -0.3873 136.0409 0.6991 0.9985 0.9907 1.0064
## 4 Retired_bin -0.0387 0.0539 -0.7179 178.6501 0.4738 0.9620 0.8656 1.0692
## 5 Volunteer_rec 0.0674 0.0295 2.2825 172.6445 0.0237 1.0697 1.0096 1.1334
## 6 Lives_alone_bin -0.1206 0.0628 -1.9226 177.3012 0.0561 0.8864 0.7837 1.0025
## 7 Phys_health_rating -0.0331 0.0401 -0.8259 176.2923 0.4100 0.9674 0.8943 1.0465
## 8 Multimorbidity_score 0.0165 0.0139 1.1875 179.6094 0.2366 1.0166 0.9893 1.0447
## 9 Mobility_needs_bin -0.0902 0.1324 -0.6811 178.8297 0.4967 0.9137 0.7049 1.1845
## 10 ABC_mean -0.0048 0.0033 -1.4298 178.5234 0.1545 0.9952 0.9888 1.0017
## 11 Subj_vision_rating_aided 0.0063 0.0366 0.1724 177.8264 0.8633 1.0063 0.9367 1.0812
## 12 Subj_hearing_loss_bin 0.0970 0.0747 1.2994 105.9267 0.1966 1.1019 0.9518 1.2756
## 13 Subj_hearing_rating_unaided_REV 0.0246 0.0382 0.6426 172.8972 0.5213 1.0249 0.9510 1.1046
## 14 Tinnitus_past_wk_bin -0.0344 0.0560 -0.6151 150.4324 0.5394 0.9662 0.8657 1.0783
## 15 PTA4_better_ear 0.0096 0.0039 2.4327 19.2745 0.0249 1.0096 1.0020 1.0174
## 16 PTA4_asym 0.0037 0.0021 1.8059 175.6367 0.0726 1.0037 0.9996 1.0078
## 17 SSQ15i_mean_REV -0.0513 0.0212 -2.4239 179.0321 0.0164 0.9500 0.9113 0.9903
## 18 Emocheq_mean 0.0016 0.0337 0.0464 151.5597 0.9630 1.0016 0.9376 1.0700
## 19 HHIES_total 0.0091 0.0046 1.9594 160.5738 0.0518 1.0091 1.0001 1.0183
## 20 SIM_mean 0.0041 0.0116 0.3558 176.2630 0.7224 1.0041 0.9815 1.0272
## 21 positive_SCI_bin -0.0882 0.0982 -0.8979 157.8400 0.3706 0.9156 0.7553 1.1099
## 22 CSRQ_mean -0.0516 0.0738 -0.6988 141.7428 0.4858 0.9497 0.8218 1.0975
## 23 PHQ4_anx_mean 0.1025 0.0546 1.8754 178.4944 0.0624 1.1079 0.9955 1.2331
## 24 PHQ4_dep_mean -0.0202 0.0721 -0.2800 167.4595 0.7798 0.9800 0.8509 1.1288
## 25 WHOQOL_overall_qol 0.0138 0.0508 0.2723 179.3228 0.7857 1.0139 0.9178 1.1200
## 26 WHOQOL_health_qol 0.0634 0.0353 1.7956 173.3409 0.0743 1.0655 0.9942 1.1418
## 27 WHO_money 0.0270 0.0272 0.9937 176.1375 0.3217 1.0274 0.9740 1.0836
## 28 Socsupp_mean 0.0287 0.0343 0.8354 155.9077 0.4048 1.0291 0.9622 1.1007
## 29 Social_network_index 0.0006 0.0197 0.0321 179.6335 0.9744 1.0006 0.9627 1.0400
## 30 Soc_part_freq 0.0706 0.0433 1.6318 165.8645 0.1046 1.0732 0.9858 1.1682
## 31 Soc_part_types -0.0157 0.0192 -0.8163 170.5264 0.4154 0.9844 0.9481 1.0222
## 32 Lonely_bin -0.0049 0.0748 -0.0659 153.1799 0.9476 0.9951 0.8594 1.1522
## 33 Motivate_mean -0.0062 0.0291 -0.2129 179.4084 0.8317 0.9938 0.9387 1.0522## Term Estimate StdError t df p OddsRatio CIlower CIupper
## 1 (Intercept) -1.3177 0.4871 -2.7050 136.8350 0.0077 0.2678 0.1031 0.6956
## 2 Gender_bin 0.1145 0.0559 2.0474 180.1686 0.0421 1.1213 1.0049 1.2512
## 3 Age 0.0067 0.0036 1.8534 236.6930 0.0651 1.0067 0.9996 1.0139
## 4 Retired_bin -0.0487 0.0518 -0.9402 250.3118 0.3480 0.9525 0.8605 1.0542
## 5 Volunteer_rec 0.0399 0.0309 1.2922 189.7278 0.1979 1.0407 0.9795 1.1057
## 6 Lives_alone_bin 0.0749 0.0612 1.2239 197.1641 0.2224 1.0778 0.9559 1.2151
## 7 Phys_health_rating 0.0277 0.0384 0.7212 133.2852 0.4720 1.0281 0.9535 1.1085
## 8 Multimorbidity_score -0.0054 0.0097 -0.5537 253.4107 0.5803 0.9946 0.9759 1.0137
## 9 Mobility_needs_bin 0.0269 0.1208 0.2223 122.7111 0.8244 1.0273 0.8107 1.3017
## 10 ABC_mean -0.0021 0.0021 -1.0411 161.2161 0.2994 0.9979 0.9938 1.0020
## 11 Subj_vision_rating_aided 0.0013 0.0327 0.0396 243.8964 0.9684 1.0013 0.9391 1.0676
## 12 Subj_hearing_loss_bin 0.0738 0.0715 1.0317 183.3870 0.3036 1.0766 0.9358 1.2385
## 13 Subj_hearing_rating_unaided_REV 0.1160 0.0348 3.3312 251.9835 0.0010 1.1230 1.0490 1.2023
## 14 Tinnitus_past_wk_bin -0.0471 0.0474 -0.9933 251.3714 0.3215 0.9540 0.8694 1.0469
## 15 PTA4_better_ear 0.0066 0.0031 2.1470 93.4544 0.0344 1.0066 1.0005 1.0128
## 16 PTA4_asym 0.0017 0.0021 0.8181 107.9354 0.4151 1.0017 0.9976 1.0058
## 17 SSQ15i_mean_REV -0.1001 0.0186 -5.3834 184.6014 0.0000 0.9047 0.8724 0.9383
## 18 Emocheq_mean -0.0072 0.0294 -0.2458 155.3778 0.8062 0.9928 0.9372 1.0517
## 19 HHIES_total 0.0091 0.0040 2.2698 118.3115 0.0250 1.0091 1.0013 1.0171
## 20 SIM_mean -0.0117 0.0116 -1.0042 181.9076 0.3166 0.9884 0.9662 1.0111
## 21 positive_SCI_bin 0.0929 0.0772 1.2026 167.4327 0.2308 1.0974 0.9433 1.2766
## 22 CSRQ_mean 0.0415 0.0727 0.5710 121.2021 0.5690 1.0424 0.9039 1.2020
## 23 PHQ4_anx_mean 0.1570 0.0523 3.0022 213.0446 0.0030 1.1700 1.0560 1.2963
## 24 PHQ4_dep_mean -0.0272 0.0580 -0.4683 209.2524 0.6401 0.9732 0.8686 1.0903
## 25 WHOQOL_overall_qol 0.0870 0.0487 1.7857 193.4626 0.0757 1.0909 0.9916 1.2002
## 26 WHOQOL_health_qol 0.0138 0.0331 0.4177 143.5408 0.6768 1.0139 0.9502 1.0819
## 27 WHO_money 0.0240 0.0274 0.8746 175.2817 0.3830 1.0243 0.9707 1.0808
## 28 Socsupp_mean -0.0012 0.0411 -0.0286 41.6853 0.9773 0.9988 0.9215 1.0826
## 29 Social_network_index 0.0003 0.0210 0.0131 145.0681 0.9896 1.0003 0.9600 1.0423
## 30 Soc_part_freq -0.0415 0.0403 -1.0298 151.6512 0.3047 0.9593 0.8865 1.0382
## 31 Soc_part_types 0.0010 0.0188 0.0556 149.3415 0.9557 1.0010 0.9648 1.0386
## 32 Lonely_bin -0.0341 0.0688 -0.4954 158.2663 0.6210 0.9665 0.8446 1.1060
## 33 Motivate_mean 0.0204 0.0308 0.6642 79.5828 0.5085 1.0206 0.9608 1.0841Legend: Asterisks denote p < 0.05; crosses denote p [0.05, 0.1]
Variable selection: Predicting HA adoption
Penalized logistic regression (LASSO) with 5-fold cross-validation was conducted across 100 lambda (penalty) values. The lambda value that led to the best-fitting model (with lowest cross-validation error) was 0.044, which corresponds to a model with 13 predictors:
Regression output (13 selected) (imputed data, n=525)
## Term Estimate StdError t df p OddsRatio CIlower CIupper
## 1 (Intercept) -0.7963 0.1793 -4.4423 466.5515 0.0000 0.4510 0.3174 0.6409
## 2 Gender_bin 0.0355 0.0325 1.0917 489.3016 0.2755 1.0361 0.9722 1.1043
## 3 Age 0.0022 0.0022 1.0205 290.7249 0.3083 1.0022 0.9979 1.0065
## 4 Volunteer_rec 0.0421 0.0182 2.3067 472.5371 0.0215 1.0430 1.0064 1.0809
## 5 Lives_alone_bin -0.0225 0.0390 -0.5760 497.0567 0.5649 0.9778 0.9058 1.0554
## 6 Subj_hearing_loss_bin 0.0784 0.0482 1.6269 292.9549 0.1048 1.0816 0.9841 1.1887
## 7 Subj_hearing_rating_unaided_REV 0.0945 0.0244 3.8755 431.6994 0.0001 1.0991 1.0478 1.1530
## 8 PTA4_better_ear 0.0083 0.0023 3.6810 67.2129 0.0005 1.0083 1.0038 1.0129
## 9 PTA4_asym 0.0031 0.0014 2.1174 138.5066 0.0360 1.0031 1.0004 1.0059
## 10 SSQ15i_mean_REV -0.0749 0.0123 -6.0967 272.3709 0.0000 0.9278 0.9057 0.9505
## 11 HHIES_total 0.0054 0.0025 2.1303 169.9426 0.0346 1.0054 1.0005 1.0104
## 12 PHQ4_anx_mean 0.0959 0.0293 3.2757 187.7804 0.0013 1.1006 1.0392 1.1657
## 13 WHO_money 0.0381 0.0178 2.1395 215.4898 0.0335 1.0388 1.0032 1.0757
## 14 Socsupp_mean 0.0268 0.0208 1.2879 333.0934 0.1987 1.0272 0.9861 1.0699Limiting the model to the 8 predictors with p < 0.05, all 8 predictors remain significant in a standard logistic regression model.
Regression output (8 selected) (imputed data, n=525)
## Term Estimate StdError t df p OddsRatio CIlower CIupper
## 1 (Intercept) -0.6127 0.1044 -5.8707 218.5124 0.0000 0.5419 0.4416 0.6649
## 2 Volunteer_rec 0.0421 0.0181 2.3210 428.5667 0.0208 1.0430 1.0066 1.0807
## 3 Subj_hearing_rating_unaided_REV 0.1115 0.0225 4.9617 379.4792 0.0000 1.1180 1.0697 1.1684
## 4 PTA4_better_ear 0.0104 0.0018 5.6517 192.1114 0.0000 1.0105 1.0069 1.0140
## 5 PTA4_asym 0.0034 0.0014 2.4128 206.3060 0.0167 1.0034 1.0007 1.0062
## 6 SSQ15i_mean_REV -0.0755 0.0123 -6.1393 279.6360 0.0000 0.9273 0.9052 0.9499
## 7 HHIES_total 0.0054 0.0025 2.1268 130.9653 0.0353 1.0054 1.0005 1.0104
## 8 PHQ4_anx_mean 0.0836 0.0291 2.8772 157.7745 0.0046 1.0872 1.0269 1.1510
## 9 WHO_money 0.0509 0.0170 2.9949 226.0709 0.0031 1.0522 1.0177 1.0879
Accuracy of model predictions
## [1] "Imputed data, 8 predictors, using median as boundary to classify 0 or 1"## predicted
## actual 0 1
## 0 252 170
## 1 11 92## [1] "Accuracy: 0.655"## [1] "Sensitivity: 0.893"## [1] "Specificity: 0.597"